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Factorization Properties in d-Dimensional Spin Glasses. Rigorous Results and Some Perspectives

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Abstract

In this paper we show that d-dimensional Gaussian spin glass models are strongly stochastically stable, fulfill the Ghirlanda-Guerra identities in distribution and the ultrametricity property.

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Acknowledgements

The authors thanks an anonymous referee for a question who led to the final remark of the conclusion. S.S. was supported by an NSA Young Investigator’s grant.

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Authors and Affiliations

  1. Università di Bologna, Piazza di Porta S. Donato 5, 40127, Bologna, Italy

    Pierluigi Contucci & Emanuele Mingione

  2. University of Alabama at Birmingham, 1300 University Boulevard, Birmingham, AL, 35294-1170, USA

    Shannon Starr

Authors
  1. Pierluigi Contucci
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  2. Emanuele Mingione
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  3. Shannon Starr
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Correspondence to Pierluigi Contucci.

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Contucci, P., Mingione, E. & Starr, S. Factorization Properties in d-Dimensional Spin Glasses. Rigorous Results and Some Perspectives. J Stat Phys 151, 809–829 (2013). https://doi.org/10.1007/s10955-013-0730-z

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  • DOI: https://doi.org/10.1007/s10955-013-0730-z

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